How mathematics trained science to expect inevitability
The previous post traced the Platonic consolidation of formal closure into ontology itself. Forms, stripped of horizon and relation, became the measure of what truly is. Reality was no longer what appeared, but what remained invariant across all appearances.
This post follows the next migration of that commitment.
Here, formal closure leaves the domain of metaphysical contemplation and enters the domain of explanation. The question is no longer what is real? but why must things happen as they do?
This is the birth of ontological necessity — the conviction that nature itself is governed by inevitable structures that compel events to unfold in only one possible way.
1. From Form to Governance
Plato’s Forms did not govern the world. They stood above it, as standards of intelligibility. But once formal invariance is treated as ontologically primary, it invites a further step: if reality is structured by invariant form, then change must be ruled by it.
This is where the concept of law enters.
A law differs from a Form in one crucial respect. A Form explains by exemplarity; a law explains by constraint. To invoke a law is to say not merely that events resemble a structure, but that they could not do otherwise.
The metaphysical expectation has shifted:
Order is no longer recognised; it is enforced.
2. Mathematics as Training in Inevitability
Mathematics plays a decisive role in this shift, not because of what it describes, but because of what it demonstrates.
A mathematical derivation does not merely show that something happens to be the case. It shows that, given the premises, the result is unavoidable. The conclusion is compelled by the structure of the system.
Repeated exposure to this form of reasoning trains a particular expectation:
that explanation should eliminate alternatives,
that understanding consists in derivation,
that to know why something happens is to show that it had to happen.
This expectation migrates seamlessly into natural philosophy.
The world, it is assumed, must be explainable in the same way mathematics is: through necessity-preserving transformations from axioms to outcomes.
3. Law as Reified Regularity
Early scientific laws are not merely summaries of observed regularities. They are treated as sources of those regularities.
This is the crucial ontological inversion.
Rather than saying:
“Bodies behave this way, and we describe the pattern mathematically,”
science increasingly says:
“Bodies behave this way because the law has this form.”
Formal regularities are reified into governing structures. Mathematical relations cease to be descriptions of how things behave and become explanations of why they must behave that way.
What began as disciplined closure now appears as necessity in nature.
4. Explanation as Derivation
With this shift, explanation acquires a new standard.
To explain a phenomenon is no longer to situate it within a relational field of causes, purposes, or contexts. It is to derive it from general principles.
Derivation promises:
universality (the same law applies everywhere),
inevitability (no alternatives are permitted),
economy (many phenomena reduced to one form).
These are mathematical virtues.
They become scientific virtues not because nature demands them, but because mathematics has taught us to equate intelligibility with necessity.
5. The Quiet Disappearance of Contingency
As law replaces form, contingency quietly recedes.
Events that do not follow cleanly from derivation are treated as:
noise,
error,
approximation,
or ignorance.
Openness is no longer a feature of reality; it is a symptom of incomplete knowledge. The more complete the science, the more inevitable the world should appear.
This is not yet modern physics. But its expectation is now firmly in place:
Reality must be such that mathematics can compel it.
6. Ontological Necessity Takes Hold
By the time early modern science emerges, the ground has already been prepared.
Nature is expected to be:
governed by invariant laws,
exhaustively describable in mathematical terms,
and ultimately reducible to necessary relations.
This expectation does not arise from experiment alone. It is inherited from a long-standing metaphysical inclination — one that mistakes the closure of formal systems for the structure of being itself.
Over-closure has learned not only to describe the world, but to command it.
7. Setting the Stage for Physics
This post marks the final preparatory step.
Once explanation is identified with mathematical derivation, physics becomes the privileged science — not because it studies matter, but because it most fully realises the ideal of necessity.
In the next post, we will finally enter modernity, where this expectation collides with infinity, singularity, and breakdown — and where mathematics, having been entrusted with ontology, begins to produce paradoxes it cannot contain.
The stage is set.
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